【Transformer系列（2）】Multi-head self-attention 多头自注意力

一、多头自注意力

多头自注意力机制与自注意力机制的区别在于，Q，K，V向量被分为了num_heads份。

实现流程
（1）根据num_heads参数将单头变成多头，获取多头注意力中的各个头的Q，K，V值
（2）Q叉乘K的转置，再使用softmax，获取attention
（3）attention叉乘V，得到输出

二、代码实现

（1）根据num_heads参数将单头变成多头，获取多头注意力中的各个头的Q，K，V值

# 每个token（Q，K，V）的尺寸
values_length = 33
# 原始单头长度
hidden_size = 768
# 单头qkv
# [33,768]
Query = np.random.rand(values_length, hidden_size)
Key = np.random.rand(values_length, hidden_size)
Value = np.random.rand(values_length, hidden_size)

# 单头 -> 分组为8个头
# [33,768] -> [33,8,96]
# 8个头
num_attention_heads = 8
# 原始单头拆分为多头后，我们单头的长度
attention_head_size = hidden_size // num_attention_heads
Query = np.reshape(Query, [values_length, num_attention_heads, attention_head_size])
Key = np.reshape(Key, [values_length, num_attention_heads, attention_head_size])
Value = np.reshape(Value, [values_length, num_attention_heads, attention_head_size])

# [33,8,96] -> [8,33,96] 头放最前面 M，H*W，C
Query = np.transpose(Query, [1, 0, 2])
Key = np.transpose(Key, [1, 0, 2])
Value = np.transpose(Value, [1, 0, 2])

（2）Q叉乘K的转置，再使用softmax，获取attention

# qv -> attention
# [8,33,96] @ [8,96,33] -> [8,33,33] [m1,n] @ [n,m2] -> [m1,m2]
scores = Query @ np.transpose(Key, [0, 2, 1])
print(np.shape(scores))
# qv+softmax -> attention
scores = soft_max(scores)
print(np.shape(scores))

（3）attention叉乘V，得到输出

# attention+v -> output
# [8,33,33] @ [8,33,96] -> [8,33,96] [m1,n] @ [n,m2] -> [m1,m2]
out = scores @ Value
print(np.shape(out))
# [8,33,96] -> [33,8,96]
out = np.transpose(out, [1, 0, 2])
print(np.shape(out))
# [33,8,96] -> [33,768]
out = np.reshape(out, [values_length , 768])
print(np.shape(out))

三、完整代码

# multi-head self-attention #
# by liushuai #
# 2024/2/6 #

import numpy as np

def soft_max(z):
    t = np.exp(z)
    a = np.exp(z) / np.expand_dims(np.sum(t, axis=-1), -1)
    return a

# 每个token（Q，K，V）的尺寸
# 相当于H*W
values_length = 33
# 原始单头深度
# 相当于Channels
hidden_size = 768
# 单头qkv
# [33,768]
Query = np.random.rand(values_length, hidden_size)
Key = np.random.rand(values_length, hidden_size)
Value = np.random.rand(values_length, hidden_size)

# 单头 -> 分组为8个头
# [33,768] -> [33,8,96]
# 8个头
num_attention_heads = 8
# 原始单头拆分为多头后，我们单头的深度
attention_head_size = hidden_size // num_attention_heads
Query = np.reshape(Query, [values_length, num_attention_heads, attention_head_size])
Key = np.reshape(Key, [values_length, num_attention_heads, attention_head_size])
Value = np.reshape(Value, [values_length, num_attention_heads, attention_head_size])

# [33,8,96] -> [8,33,96] 头放最前面 M，H*W，C
Query = np.transpose(Query, [1, 0, 2])
Key = np.transpose(Key, [1, 0, 2])
Value = np.transpose(Value, [1, 0, 2])

# qv -> attention
# [8,33,96] @ [8,96,33] -> [8,33,33] [m1,n] @ [n,m2] -> [m1,m2]
scores = Query @ np.transpose(Key, [0, 2, 1])
print(np.shape(scores))
# qv+softmax -> attention
scores = soft_max(scores)
print(np.shape(scores))

# attention+v -> output
# [8,33,33] @ [8,33,96] -> [8,33,96] [m1,n] @ [n,m2] -> [m1,m2]
out = scores @ Value
print(np.shape(out))
# [8,33,96] -> [33,8,96]
out = np.transpose(out, [1, 0, 2])
print(np.shape(out))
# [33,8,96] -> [33,768]
out = np.reshape(out, [values_length , 768])
print(np.shape(out))